Right before chicks hatch, they have just absorbed the last of the yolk. This sustains them during their journey, for up to three days, so that's why they need to ship at that time, when the yolk will sustain them.
The reason nature works this way is that if they were hatching beneath a mother hen, this would enable the early hatchers to survive without eating and drinking until mother finished hatching the rest of the eggs. She can't get up from the nest until the entire hatching is over, or else the last babies would die in their shells, unable to hatch without their mother's warmth. It's for this reason that shipping chicks that are more than one day old is unsafe, because after that, the babies don't have the stores needed to survive the journey.
Once chickens reach 6 weeks or so, they can maintain their own body temperatures, so once they reach that age, it is safe to ship them as juvenile birds (not chicks). We usually have two or three batches of juvenile birds available each year at various times. Read in the related questions below for more details, or click on the "6-week-olds" subcategory at the left of this page in the blue navigation bar to check current juvenile availability. (If the category is not there, we don't have any batches available right now.)
When it comes to shipping baby chicks, though, we can only ship them when they have just hatched, so they will arrive at their destination safely. Once they've reached juvenile status, it's safe to ship them again.